Pricing Stock Options by Bivariate Binomial Lattices

雙變數二元樹之股價選擇權評價模型

葉宗穎(Chung-Ying Yeh) ； 葉仕國(Shih-Kuo Yeh) ； 朱漢興(Hann-Shing Ju)

《財務金融學刊》 21卷1期 (2013/03) Pp. 53-81

https://doi.org/10.6545/JFS.2013.21(1).3

摘要

股價選擇權的設計，必須使用樹型圖等數值方法才能有效的進行評價。選擇權的評價必須考慮股價及市場利率兩個變數，因此在樹型圖的建構及計算上往往較單變數的樹型圖要來得複雜。本研究提出一個雙變數二元樹的作法，採用遠期利率曲線隨著時間所積分出來的面積取代擴散過程中的漂移項，精確而有效率地求出股價選擇權的價格。

關鍵字

二元樹 ； 遠期利率曲線 ； 選擇權評價 ； 隨機利率

並列摘要

Pricing stock options by using the binomial lattice method still poses a significant challenge in the finance literature. This is particularly true for the bivariate binomial lattice method that simultaneously allows for stock prices and interest rates to be stochastic. This article introduces a more efficient bivariate binomial lattice method to price stock options. The proposed approach simply replaces the drift term of the stock price process by the integration of the forward rate curve over the horizon of the option's maturity. The numerical simulation studies as well as the theoretical justification show that the option prices computed by the proposed lattice approach can effectively and accurately converge.

並列關鍵字

Binomial tree ； forward rate curve ； option pricing ； stochastic interest rate

參考文獻

Amin, Kaushik I.,Jarrow, Robert A.(1992).Pricing option on risky assets in a stochastic interest rate economy.Mathematical Finance.2,217-237.

Black, Fischer S.,Scholes, Myron S.(1973).The pricing of options and corporate liabilities.Journal of Political Economy.81,637-654.

Boyle, Phelim P.(1986).Options valuation using a three-jump process.International Option Journal.3,7-12.

Boyle, Phelim P.(1988).A lattice framework for option pricing with two state variables.Journal of Financial and Quantitative Analysis.23,1-12.

Cox, John C.,Ross, Stephen A.,Rubinstein, Mark(1979).Option pricing: a simplified approach.Journal of Financial Economics.7,229-263.